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Sagot :

Answer:

(-3,0)

(-1.5,0)

(3,0)

(0,-27)

Step-by-step explanation:

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Answer:

Step-by-step explanation:

As it is a third order polynomial, we expect no more than three x axis touches or three factors.

factors have a form of (ax¹ + bx⁰)

As 27 is negative, we will have only one factor with a negative x⁰ value meaning only one crossing point is positive. The other two must be negative and have positive x⁰ values

as the x³ term has a multiplier of 2, the likely multipliers for the x¹ terms are 2, 1, 1

p(x) = ( ?x + ?)(?x + ?)(?x - ?)

Let's guess that a factor is (x + 3)

                    2x² - 3x - 9  

x + 3 | 2x³ + 3x² - 18x  - 27

     -   (2x³ + 6x²)

                   -3x² - 18x

                 - (-3x² - 9x )

                             -9x - 27

                          - (-9x - 27)

                                        0

so (x + 3) is a factor and x = -3 is a zero

We are left with a quadratic which we can use the formula on

2x² - 3x - 9

x = (3 ±√(3² - 4(2)(-9))) / (2(2))

x = (3 ±√(81)) / 4

x = (3 ± 9) / 4

x = 12/4 = 3

or

x = -6/4 = -1.5

so the zeros are at -3, -1.5, and 3